Compressed Sensing for
Energy-Efficient Wireless Telemonitoring of
Non-Invasive Fetal ECG via Block Sparse Bayesian Learning,
by Zhilin
Zhang, Tzyy-Ping Jung, Scott Makeig,
Bhaskar D. Rao, accepted by IEEE Trans. Biomedical Engineering.
Note that there are two groups of works on compressed sensing of ECG. One is the ECG compression (just like video compression, image compression, etc). Most works actually belong to this group. They generally use some MIT-BIH datasets, which are very clean (noise is removed).
Another group is compressed sensing of ECG for energy-efficient wireless telemonitoring
. There are only few works in this group. Our work belongs to this group. In this group the ECG data is always contaminated by noise and artifacts ('signal noise').
This is because the goal of telemonitoring is to allow people to walk
and even exercise freely, and thus strong noise and artifacts caused by
muscle and electrode movement are not evitable. Consequently, the raw
ECG recordings are not sparse in the time domain and also not sparse in
the transformed domains (e.g. the wavelet domain, the DCT domain).
However, the strict constraint on energy consumption (and design issues,
etc) of telemonitoring systems does not encourage filtering or other
preprocessing before compression. Or, put in another way, if energy
consumption and design issues are not problems, CS may have no
advantages over traditional methods. Thus, CS algorithms have to recover
non-sparse signals for this application. It turns out that the problem
is very challenging.
Our work not only solves this challenging problem, but also has some interesting mathematical meanings:
By
linear algebra, there are infinite solutions to the underdetermined
problem y=Ax. When the true solution x0 is sparse, using CS algorithms
it is possible to find it. But when the true solution x0 is non-sparse,
finding it is more challenging and new constraints/assumptions are
called for. This work shows that when exploiting the unknown block
structure and the intra-block correlation of x0, it is possible to find a
solution x_est which is very close to the true solution x0. These
findings raise new and interesting possibilities for signal compression
as well as theoretical questions in the subject of sparse and non-sparse
signal recovery from a small number of measurements y.
文章的摘要如下:
Fetal ECG (FECG)
telemonitoring is an important branch in telemedicine. The design of a
telemonitoring system via a wireless body-area network with low energy
consumption for ambulatory use is highly desirable. As an emerging
technique, compressed sensing (CS) shows great promise in
compressing/reconstructing data with low energy consumption. However,
due to some specific characteristics of raw FECG recordings such as
non-sparsity and strong noise contamination, current CS algorithms
generally fail in this application.
This work proposes to use
the block sparse Bayesian learning (BSBL) framework to
compress/reconstruct non-sparse raw FECG recordings. Experimental
results show that the framework can reconstruct the raw recordings with
high quality. Especially, the reconstruction does not destroy the
interdependence relation among the multichannel recordings. This ensures
that the independent component analysis decomposition of the
reconstructed recordings has high fidelity. Furthermore, the framework
allows the use of a sparse binary sensing matrix with much fewer nonzero
entries to compress recordings. Particularly, each column of the matrix
can contain only two nonzero entries. This shows the framework,
compared to other algorithms such as current CS algorithms and wavelet
algorithms, can greatly reduce code execution in CPU in the data
compression stage.